CSs have been theoretically predicted and recently experimentally demonstrated in broad area, vertical cavity driven semiconductor lasers (VCSELs) slightly below the lasing threshold. Above threshold, the simple adiabatic elimination of the polarization variable is not correct, leading to oscillatory instabilities with a spuriously high critical wave-number. To achieve real insight on the complete dynamical problem, we study here the complete system of equations and find regimes where a Hopf instability, typical of lasers above threshold, affects the lower intensity branch of the homogeneous steady state, while the higher intensity branch is unstable due to a Turing instability. Numerical results obtained by direct integration of the dynamical equations show that writable/erasable CSs are possible in this regime, sitting on unstable background